What Does SPAD Afterpulsing Actually Tell Us About Defects in InP? Mark Itzler , Mark Entwistle, and Xudong Jiang SPW2011 – June 2011
Feb 11, 2016
What Does SPAD Afterpulsing Actually
Tell Us About Defects in InP?
Mark Itzler, Mark Entwistle, and Xudong Jiang
SPW2011 – June 2011
Princeton Lightwave Inc.SPW2011 – June 2011
Presentation Outline
50 MHz photon counting with RF matched delay line scheme Afterpulse probability (APP) dependence on hold-off time Fitting of APP data
inadequacy of legacy approach assuming one or few traps new fitting based on broad trap distribution
Implications of APP modeling for trap distributions Summary
2
Princeton Lightwave Inc.SPW2011 – June 2011
i-InGaAs absorption
n+-InP buffer
n-InGaAsP grading n-InP charge
i-InP cap
p+-InP diffused region
multiplication region
SiNx passivation p-contact metallization
n+-InP substrate anti-reflection coating n-contact metallization
optical input
Afterpulsing: increased DCR at high rate Single photon detection by avalanche multiplication in SPADs Avalanche carriers trapped at defects in InP multiplication region Carrier de-trapping at later times initiates “afterpulse” avalanches Serious drawback of afterpulsing → limitation on counting rate
Long hold-off time
# of trapped carriers
primary avalanche
afterpulsesshort hold-off
time
# of trapped carriers
trap sites located in multiplication region
Ec
Ev
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Princeton Lightwave Inc.SPW2011 – June 2011
New results for RF delay line circuit
Enhance matched delay line circuit to operate at higher repetition rate Inverted and non-inverted RF reflections cancel transients Based on existing PLI product platform
Bethune and Risk, JQE 36, 340 (2000)
Cancel transient response synchronous with photon arrival
Temporally gate out leading and trailing transients
Set threshold for remaining avalanche signal
4
Princeton Lightwave Inc.SPW2011 – June 2011
1E-4
1E-3
1E-2
1E-1
0% 10% 20% 30% 40%
After
puls
e Pr
obab
ility
Photon Detection Efficiency
50 MHz33 MHz10 MHz1 MHz
PER DETECTED PHOTON
Matched delay line solution to 50 MHz Extension of cancellation scheme to higher frequencies
More precise cancellation for reduced detection threshold → detect smaller avalanches Higher speed components to enable 50 MHz board-level operation
Measure cumulative afterpulsing using odd gates “lit”, even gates “dark” Take all counts in even gates above dark count background to be afterpulses
OLD Performance (1 ns gate duration) NEW Performance (1 ns gate duration)
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
5% 10% 15% 20% 25% 30%Photon Detection Efficiency
Afte
rpul
se P
roba
bilit
y
( per
1 n
s ga
te p
ulse
)
10 MHz5 MHz2 MHz1 MHz0.5 MHz
• Absence of afterpulsing “runaway” indicates higher frequencies can be achieved5
Princeton Lightwave Inc.SPW2011 – June 2011 6
“Double-pulse” afterpulse measurement Use “time-correlated carrier counting” technique to measure afterpulses Trigger single-photon avalanches in 1st gate Measure probability of afterpulse in 2nd gate at Tn
Use range of Tn to determine dependence of afterpulse probability on time following primary avalanche
Double-pulse (“pump-probe”) methodT1
≈
Cova, Lacaita, Ripamonti, EDL 12, 685 (1991)
T2≈
Afte
rpul
se
prob
abili
ty
TimeT1 T2
Princeton Lightwave Inc.SPW2011 – June 2011
FPGA-based data acquisition Use FPGA circuitry to control gating and data collection Generalize double-pulse method to many gates
Capture afterpulse counts in up to 128 gates following primary avalanche Temporal spacing of gates determined by gate repetition rate
Allows capture of afterpulse count in any gate after avalance No need to step gate position as in double-pulse method
1 ns gates
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1 2 3 4 5 6 126 127 128 1 2≈50 MHz:
20 ns
25 MHz:
1 2 3 128 1
≈40 ns
Princeton Lightwave Inc.SPW2011 – June 2011
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE = 20%1 ns gates
FPGA-based afterpulse measurements Obtain afterpulsing probability data at 5 frequencies for 128 gates
All frequencies
8
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
Time following primary avalanche (ns)
50 MHz
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
Time following primary avalanche (ns)
40 MHz
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
Time following primary avalanche (ns)
33 MHz
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
Time following primary avalanche (ns)
25 MHz
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
Time following primary avalanche (ns)
10 MHz
50 MHz
40 MHz
33 MHz 25 MHz 10 MHz
APP ~ 1% at 30 ns
Princeton Lightwave Inc.SPW2011 – June 2011
Legacy approach to afterpulse fitting Try to fit afterpulse probability (APP) data with exponential fit
Physically motivated by assumption of single dominant trap
Single exponential curve generally fits range of ~5X in time
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE = 20%1 ns gates
APP1 exp(-t/τ1)
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Princeton Lightwave Inc.SPW2011 – June 2011
Legacy approach to afterpulse fitting Try to fit afterpulse probability (APP) data with exponentials
Physically motivated by assumption of single dominant trap Single exponential not sufficient; assume second trap
Single exponential curve generally fits range of ~5X in time
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE = 20%1 ns gates
APP2 exp(-t/τ2)
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Princeton Lightwave Inc.SPW2011 – June 2011
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE = 20%1 ns gates
Legacy approach to afterpulse fitting Try to fit afterpulse probability (APP) data with exponentials
Physically motivated by assumption of single dominant trap Single exponential not sufficient; assume second trap Still need third exponential to fit full data set
Single exponential curve generally fits range of ~5X in time
APP3 exp(-t/τ3)
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Princeton Lightwave Inc.SPW2011 – June 2011
Legacy approach to afterpulse fitting Can achieve reasonable fit with several exponentials …but choice of time constants is completely arbitrary!
→ depends on range of times used in data set Our assertion: No physical significance to time constants in fitting
→ simply minimum set of values to fit the data set in question
APP = C1exp(-t/τ1) + C2exp(-t/τ2) + C3exp(-t/τ3)
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE = 20%1 ns gates
τ1 = 30 ns
τ2 = 120 ns
τ3 = 600 ns
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Princeton Lightwave Inc.SPW2011 – June 2011
What other functions describe APP?
Good fit for simple power law T-α with α ≈ -1→ Is power law behavior found for other afterpulsing measurements?→ Is the power law functional form physically significant?
APP = C T-α
y = 0.52x-1.07
1E-5
1E-4
1E-3
1E-2
1E-1
10 100 1000
After
pusl
e pr
obab
ility
per
de
tect
ed p
hoto
n p
er g
ate
Time following primary avalanche (ns)
50 MHz40 MHz33 MHz25 MHz10 MHz
PDE ~ 20%1 ns gates
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Princeton Lightwave Inc.SPW2011 – June 2011
y = 3.44x-1.03
y = 2.20x-1.05
y = 0.74x-1.09
1E-4
1E-3
1E-2
1E-1
1E+0
10 100 1000
After
puls
e pr
obab
ility
Time following primary avalanche (ns)
3 ns gate2 ns gate1 ns gate
UVA data~30% PDE
Afterpulsing data from Univ. Virginia
Good fit for power law T-α with α ≈ -1.0 to -1.1
data from Joe Campbell, UVA
Double-pulse method
PLI SPADs
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Princeton Lightwave Inc.SPW2011 – June 2011
y = 2.92x-1.16
y = 0.49x-1.21
y = 0.13x-1.24
y = 0.06x-1.25
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1 10 100 1000
After
puls
e Pr
obab
ility
Time following primary avalanche (ns)
1.50 ns gate1.00 ns gate0.63 ns gate0.50 ns gate
NIST data~15% PDE
Afterpulsing data from NIST
Good fit for power law T-α with α ≈ -1.15 to -1.25
data from Alessandro Restelli and Josh Bienfang, NIST
Double-pulse method
PLI SPADs
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Princeton Lightwave Inc.SPW2011 – June 2011
y = 237.66x-1.38
0.001
0.01
0.1
1
10 100 1000
Nor
mal
ized
After
puls
e Pr
obab
ility
Time following primary avalanche (ns)
Nihon U. data213 K
Afterpulsing data from Nihon Univ.
Good fit for power law T-α with α = -1.38
data from Naota Namekata, Nihon U.
Autocorrelation test of time-tagged data
PLI SPADs
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Princeton Lightwave Inc.SPW2011 – June 2011
Literature on InP trap defects
Literature on defects in InP describes dense spectrum of levels
Instead of assuming one or a few dominant trap levels: → consider implications of a broad distribution for τ
i-InGaAs absorption
n+-InP buffer
n-InGaAsP grading n-InP charge
i-InP cap
p+-InP diffused region
multiplication region
SiNx passivation p-contact metallization
n+-InP substrate anti-reflection coating n-contact metallization
optical input
Deep-level traps in multiplication region
Ec – 0.24 eVEc – 0.30 eVEc – 0.37 eVEc – 0.40 eV
Ec – 0.55 eV
W. A. Anderson and K. L. Jiao, in “Indium Phosphide and Related Materials: Processing, Technology, and Devices”, A. Katz (ed.) (Artech House, Boston, 1992)
Early work
Later work
Radiation effects
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Princeton Lightwave Inc.SPW2011 – June 2011
Implications of trap distribution on APP Develop model for APP with distribution of detrap rates R ≡ 1/τ
– APP related to change in trap occupation: dN/dt ~ R exp(-t R)– Integrate over detrapping rate distribution D(R)
→ APP ~ ∫ dR D(R) R exp(-t R)
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D(R)
RR0
D(R)
RR0
D(R)
R
D(R)
R
δ(R – R0)single trap
“Uniform”
Normal “Inverse”D(R) α 1/R
narrowest distribution
widest distribution
Princeton Lightwave Inc.SPW2011 – June 2011
Implications of trap distribution on APP
“Single trap” leads to exponential behavior– Fitting requires multiple exponentials and is arbitrary
Normal distribution is similar to single trap– Gaussian broadening of δ(R – R0) doesn’t change exponential behavior
“Uniform” and “inverse” distributions can be solved analytically– Require assumptions for a few model parameters
Minimum detrapping time: τmin = 10 ns Maximum detrapping time: τmax = 10 µsNumber of trapped carriers: n = 5Detection efficiency: 20%
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just sample values;can be generalized
Princeton Lightwave Inc.SPW2011 – June 2011
y = 200.93x-2.00y = 25.23x-1.18
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
10 100 1000 10000
Nor
mal
ized
after
puls
ing
prob
abili
ty
Time following primary avalanche (ns)
Inverse
Uniform
Modeling results for APP APP results for Uniform and Inverse detrap rate distributions D(R) APP behavior fit well by T-α for 10 ns to 10 µs
– Value of α depends on model parameter values, but α is well-bounded
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Inverse D(R): T-α with 1.05 < α < 1.30
Uniform D(R): T-α with 1.9 < α < 2.1
Princeton Lightwave Inc.SPW2011 – June 2011
Insights from modeling of APP Inverse distribution provides correct power law behavior
– More traps with slower release rates D(R) α 1/R– Other distributions considered do not agree with data
Inverse distribution not necessarily a unique solution– But it provides more accurate description than single trap or uniform
Slower falloff of APP with hold-off time for Inverse distribution– Need longer hold-off times to achieve same relative decrease in total AP
Other possible explanations for power law behavior to explore– Role of field-assisted detrapping, especially in non-uniform E-field– Model in literature cites power law behavior for “correlated” detrapping
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D(R)
R
A. K. Jonscher,Sol. St. Elec. 33, 139 (1990)
Princeton Lightwave Inc.SPW2011 – June 2011
Afterpulsing data on Silicon SPADs
Neither power law nor exponential provide particularly good fit! Nature of defects in Si SPADs may be categorically different than for InP
data from Massimo Ghioni, Politecnico di Milano
Double-pulse method
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y = 0.0002e-0.005x
y = 0.21x-1.54
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
10 100 1000
Afte
rpul
sing
Pro
babi
lity
Den
sity
(ns
-1)
Time (ns)
10
10
10
10
10
10
-7
-6
-5
-4
-3
-2
Silicon SPADsT = -25 C, Pap = 6%
Power law
Exponential
Princeton Lightwave Inc.SPW2011 – June 2011
Summary
Reached 50 MHz photon counting with RF matched delay line scheme Significant further repetition rate increases should be feasible
Fitting of APP data with multiple exponentials not physically meaningful Extracted detrapping times are arbitrary, depend on hold-off times used Literature on defects in InP suggests possibility of broad distribution of defects
Consistent power law behavior of APP data found by various groups APP vs. time T described by T-α with α ~ 1.2 ± 0.2
Assumption of “inverse” distribution D(R) α 1/R for detrapping rate R provides best description of data among distributions considered so far Not unique, but establishes general behavior May be other models that predict power law APP behavior for dominant trap Further modeling can predict behavior for different operating conditions
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Princeton Lightwave Inc.SPW2011 – June 2011
BACK-UP SLIDES
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Princeton Lightwave Inc.SPW2011 – June 2011
Vertical structure to realize SAGCM structure for well-designed APD Multiplication gain: high field for impact ionization Carrier drift in absorber: low but finite absorber field Avoid of tunneling in all layers Eliminate interface carrier pile-up
Control of 3-D electric field distribution to avoid edge breakdown
Electric field engineering in APDs
i-
n+-InP buffer
n -InGaAsP gradingn- InP charge
i-InP cap
SiNx passivation p-contact metallization
n+-InP substrate
anti-reflection coating n-contact metallization
optical input
E
InGaAs absorption
multiplication region
p+-InP diffused region
Schematic design for InGaAs/InP SPAD for 1.5 μm photon counting
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